Parameterization of All Output-Rectifying Retrofit Controllers
Hampei Sasahara, Takayuki Ishizaki, Jun-ichi Imura

TL;DR
This paper provides a comprehensive parameterization of all output-rectifying retrofit controllers, enabling easier design and understanding of structured controllers in distributed systems, by generalizing existing methods through state projection and inverse systems.
Contribution
It introduces a tractable, generalized parameterization of output-rectifying retrofit controllers applicable to the general output-feedback case, expanding previous constrained approaches.
Findings
All retrofit controllers can be characterized as a constrained Youla parameterization.
An unconstrained parameterization is derived under a technical measurability assumption.
Output-rectifying retrofit controllers can be designed even in the general output-feedback case.
Abstract
This study investigates a parameterization of all output-rectifying retrofit controllers for distributed design of a structured controller. It has been discovered that all retrofit controllers can be characterized as a constrained Youla parameterization, which is difficult to solve analytically. For synthesis, a tractable and insightful class of retrofit controllers, referred to as output-rectifying retrofit controllers, has been introduced. An unconstrained parameterization of all output-rectifying retrofit controllers can be derived under a technical assumption on measurability of particular signals. The aim of this note is to reveal the structure of all output-rectifying retrofit controllers in the general output-feedback case. It is found out that the existing developments can be generalized based on the notions of state projection and an inverse system. The result leads to the…
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